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检索条件"主题词=Semidefinite Programming"

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A bound on the minimum rank of solutions to sparse linear matrix equations

A bound on the minimum rank of solutions to sparse linear ma...

引用

American Control Conference

作者： Raphael Louca Subhonmesh Bose Eilyan Bitar School of Electrical and Computer Engineering Cornell University Ithaca NY 14853 USA Department of Electrical and Computer Engineering University of Illinois Champaign 61820 USA

ISBN: (纸本)9781467386838

We derive a new upper bound on the minimum rank of matrices belonging to an affine slice of the positive semidefinite cone, when the affine slice is defined according to a system of sparse linear matrix equations. It is shown that a feasible matrix whose rank is no greater than said bound can be computed in polynomial time. The bound depends on both the number of linear matrix equations and their underlying sparsity pattern. For certain problem families, this bound is shown to improve upon well known bounds in the literature. Several examples are provided to illustrate the efficacy of this bound.

关键词： chordal graphs rank minimization semidefinite programming sparse linear matrix equations LINEAR EQUATION,MATRIX Bound Rank of data Positive semi-definite Affine In-law slicing

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Sparsest cut on quotients of the hypercube 2011

Sparsest cut on quotients of the hypercube

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Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119

作者： Alexandra Kolla James R. Lee Microsoft Research Redmond WA University of Washington Seattle WA

ISBN: (纸本)9781920682989

We present a simple construction and analysis of an Ω(log log N) integrality gap for the well-known Sparsest Cut semi-definite program (SDP). This holds for the uniform demands version (i.e. edge expansion). The same quantitative gap was proved earlier by Devanur, Khot, Saket, and Vishnoi [STOC 2006], following an integrality gap for non-uniform demands due to Khot and Vishnoi [FOCS 2005]. These previous constructions involve a complicated SDP solution and analysis, while our gap instance, vector solution, and analysis are somewhat simpler and more ***, our approach is rather general, and provides a variety of different gap examples derived from quotients of the hypercube. It also illustrates why the lower bound is stuck at Ω(log log N), and why new ideas are needed in order to derive stronger examples.

关键词： Sparsest Cut semidefinite programming integrality gap

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Tight semidefinite Relaxation for Combinatorial Optimization in UWB Multiuser Detection Systems

Tight Semidefinite Relaxation for Combinatorial Optimization...

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IEEE Vehicular Technology Conference

作者： Chanfei Wang Tiejun Lv Hui Gao Anzhong Hu Key Laboratory of Trustworthy Distributed Computing and Service Ministry of Education School of Information and Communication Engineering Beijing University of Posts and Telecommunications

ISBN: (纸本)9781479944811

In this paper, two near-optimal detectors based on the convex optimization algorithm are proposed for multiuser detection (MUD) in the ultra-wide bandwidth (UWB) systems. The first detector performs semidefinite relaxation (SDR) to approximate the optimum multiuser detection (OMD) which is a nondeterministic polynomial time hard (NP-hard) problem. When the cutting planes generation algorithm is employed to strengthen the relaxation of the SDR, a tight MUD detector for combinatorial optimization is obtained by adding triangle inequalities to the well-known SDR in strict feasible region. Simulations demonstrate that the semidefinite programming (SDP) approaches can provide bit error rate (BER) performance close to the OMD efficiently using the interior point method, and the tight detector provides a better BER performance than the previous detector with a slightly higher complexity.

关键词： combinatorial mathematics computational complexity error statistics mathematical programming multiuser detection relaxation ultra wideband communication BER MUD detector NP-hard problem OMD SDP SDR UWB multiuser detection systems bit error rate combinatorial optimization convex optimization algorithm generation algorithm near-optimal detectors nondeterministic polynomial time hard problem optimum multiuser detection semidefinite programming semidefinite relaxation ultra-wide bandwidth systems Bit error rate Complexity theory Detectors Multiuser detection Optimization programming Vectors Bit error rate Multiuser detection SDPR gene OMD gene combinatorial mathematics Nondeterministic polynomial-time hard Ultra wideband communication Service Discovery Protocol Optimization algorithms Complexity theory programming complexity classes detector relaxation Relaxation

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Learning Stable Evolutionary PDE Dynamics: A Scalable System Identification Approach

Learning Stable Evolutionary PDE Dynamics: A Scalable System...

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Control Technology and Applications (CCTA),

作者： Diyou Liu Mohammad Khosravi Delft Center for Systems and Control Delft University of Technology Delft Netherlands

ISBN: (数字)9798350370942

ISBN: (纸本)9798350370959

In this paper, we discuss the learning and discovery problem for the dynamical systems described through stable evolutionary Partial Differential Equations (PDEs). The main idea is to employ a suitable learning approach for creating a map from boundary conditions to the corresponding output. More precisely, in order to accurately uncover the evolutionary PDE dynamics, we propose a scheme that employs large-scale system identification to construct such a map using sufficiently informative measurements. Accordingly, we first develop a scalable implementation for the subspace identification method, enforcing stability on the identified system. To this end, numerical optimization techniques such as coordinate descent, randomized singular value decomposition, and large-scale semidefinite programming are employed. The performance and complexity of the resulting scheme are discussed and demonstrated through numerical experiments on generic identification examples. Following this, we validate the effectiveness of the proposed approach on an example of a stable evolutionary partial differential equation. The numerical results confirm the efficacy of the proposed learning scheme.

关键词： semidefinite programming Partial differential equations Memory management Stability analysis System identification Large-scale systems Noise measurement

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Two-Dimensional Grid-Free Algorithm for Separation of Underwater Acoustic Raypath

Two-Dimensional Grid-Free Algorithm for Separation of Underw...

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IEEE International Conference on Signal and Image Processing (ICSIP)

作者： Fengyan Zhong Zhichen Li Chao Yang The Laboratory of Image Science and Technology Southeast University Nanjing China

ISBN: (数字)9798350350920

ISBN: (纸本)9798350350937

In this paper, a high resolution raypath separation algorithm is proposed in the context of ocean acoustic tomography. By exploiting atomic norm theory, signals were sparsely represented in a two-dimensional continuous space of angle and delay, and a convex semidefinite programming (SDP) model with atomic norm constraints is established. The dual SDP problem of this model is derived from the perspective of dual norms. The proposed algorithm does not require grid division of the estimation domain, thus eliminating the grid mismatch problem. Experimental results show that, compared to the two-dimensional conventional compressive beamforming, the presented approach improves separation accuracy.

关键词： Image coding Accuracy semidefinite programming Array signal processing Oceans Tomography Delays

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Convex algebraic geometry and semidefinite optimization 13

Convex algebraic geometry and semidefinite optimization

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Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation

作者： Pablo A. Parrilo Massachusetts Institute of Technology Cambridge MA USA

ISBN: (纸本)9781450320597

In the past decade there has been a surge of interest in algebraic approaches to optimization problems defined by multivariate polynomials. Fundamental mathematical challenges that arise in this area include understanding the structure of nonnegative polynomials, the interplay between efficiency and complexity of different representations of algebraic sets, and the development of effective algorithms. Remarkably, and perhaps unexpectedly, convexity provides a new viewpoint and a powerful framework for addressing these questions. This naturally brings us to the intersection of algebraic geometry, optimization, and convex geometry, with an emphasis on algorithms and computation. This emerging area has become known as convex algebraic *** tutorial will focus on basic and recent developments in convex algebraic geometry, and the associated computational methods based on semidefinite programming for optimization problems involving polynomial equations and inequalities. There has been much recent progress, by combining theoretical results in real algebraic geometry with semidefinite programming to develop effective computational approaches to these problems. We will make particular emphasis on sum of squares decompositions, general duality properties, infeasibility certificates, approximation/inapproximability results, as well as survey the many exciting developments that have taken place in the last few years.

关键词： convex optimization convex algebraic geometry semidefinite programming multivariate polynomials

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Coordinated Sparse Precoding for Distributed Integrated Sensing and Communication Systems

Coordinated Sparse Precoding for Distributed Integrated Sens...

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IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

作者： R. S. Prasobh Sankar Soumyadeep Chatterjee Sundeep Prabhakar Chepuri Indian Institute of Science Bengaluru India

ISBN: (数字)9798350393187

ISBN: (纸本)9798350393194

In this paper, we address the problem of transmit precoding in distributed integrated sensing and communication (DISAC) systems. We introduce Generalized Sparse Coordinated MultiPoint transmission (GS-CoMP), a sparse precoding-based coordination strategy for ISAC. The aim is to achieve a backhaul rate reduction by designing the subset of base stations (BS) serving each user (UE). We design transmit precoders to minimize a weighted sum of total transmit power and backhaul rate while guaranteeing desired communication and radar sensing signal-to-interference-plus-noise ratios (SINRs). The underlying precoding problem is non-convex. We present a convex-relaxation-based solver to obtain the precoders and BS-UE association. Through numerical simulations, we demonstrate that GS-CoMP outperforms DISAC systems without cooperation while requiring a significantly reduced backhaul rate compared to DISAC systems with full cooperation.

关键词： Wireless communication semidefinite programming Precoding Interference Radar Signal processing Integrated sensing and communication Numerical simulation Backhaul networks Signal to noise ratio

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RNN Controller for Lane-Keeping Systems with Robustness and Safety Verification

RNN Controller for Lane-Keeping Systems with Robustness and ...

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American Control Conference (ACC)

作者： Ying Shuai Quan Jin Sung Kim Chung Choo Chung Dept. of Electrical Engineering Hanyang University Seoul Korea Dept. of Electrical Engineering Chalmers University of Technology Gothenburg Sweden Dept. of Electrical Engineering Hanyang University Seoul Republic of Korea

ISBN: (数字)9798350382655

ISBN: (纸本)9798350382662

This paper proposes a Recurrent Neural Network (RNN) controller for lane-keeping systems, effectively handling model uncertainties and disturbances. First, quadratic constraints cover the nonlinearities brought by the RNN controller, and the linear fractional transformation method models the dynamics of system uncertainties. Second, we prove the robust stability of the lane-keeping system in the presence of uncertain vehicle speed using a linear matrix inequality. Then, we define a reachable set for the lane-keeping system. Finally, to confirm the safety of the lane-keeping system with tracking error bound, we formulate semidefinite programming to approximate the outer set of the reachable set. Numerical experiments demonstrate that this approach confirms the stabilizing RNN controller and validates the safety with an untrained dataset with untrained varying road curvatures.

关键词： Training Uncertainty Recurrent neural networks semidefinite programming Robust stability Roads Robustness

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Tight size-degree bounds for sums-of-squares proofs 15

Tight size-degree bounds for sums-of-squares proofs

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Proceedings of the 30th Conference on Computational Complexity

作者： Massimo Lauria Jakob Nordström KTH Royal Institute of Technology Stockholm Sweden

ISBN: (纸本)9783939897811

We exhibit families of 4-CNF formulas over n variables that have sums-of-squares (SOS) proofs of unsatisfiability of degree (a.k.a. rank) d but require SOS proofs of size nΩ(d) for values of d = d(n) from constant all the way up to nδ for some universal constant δ. This shows that the nO(d) running time obtained by using the Lasserre semidefinite programming relaxations to find degree-d SOS proofs is optimal up to constant factors in the exponent. We establish this result by combining NP-reductions expressible as low-degree SOS derivations with the idea of relativizing CNF formulas in [Krajíček '04] and [Dantchev and Riis '03], and then applying a restriction argument as in [Atserias, Müller, and Oliva '13] and [Atserias, Lauria, and Nordström '14]. This yields a generic method of amplifying SOS degree lower bounds to size lower bounds, and also generalizes the approach in [ALN14] to obtain size lower bounds for the proof systems resolution, polynomial calculus, and Sherali-Adams from lower bounds on width, degree, and rank, respectively.

关键词： sums-of-squares SOS size semidefinite programming resolution rank positivstellensatz proof complexity lower bound lasserre degree clique

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semidefinite Optimization for Transient Analysis of Queues 10

SemidefInite Optimization for Transient Analysis of Queues

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SIGMETRICS 2010

作者： Takayuki Osogami Rudy Raymond IBM Research - Tokyo Yamato-shi Japan

ISBN: (纸本)9781450300384

We derive an upper bound on the tail distribution of the transient waiting time for the GI/GI/1 queue from a formulation of semidefinite programming (SDP). Our upper bounds are expressed in closed forms using the first two moments of the service time and the interarrival time. The upper bounds on the tail distributions are integrated to obtain the upper bounds on the corresponding expectations. We also extend the formulation of the SDP, using the higher moments of the service time and the interarrival time, and calculate upper bounds and lower bounds numerically.

关键词： semidefinite programming duality G/G/l queue tran-sient bounds moments occupation measure

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